In order to have transactions executed and recorded on blockchains such as the Ethereum Mainnet, fees expressed in crypto-currency units of the blockchain must be paid. One can buy crypto-currency called Ether of the Ethereum blockchain from exchanges and pay for the transaction fees. In the case of test networks (such as Rinkeby) or scientific research blockchains (such as Bloxberg), free crypto-currency, Ether, is distributed to users via faucets. Since transaction slots on the blocks, storage and smart contract executions are consuming blockchain resources, Ethers are distributed by fixed small amounts to users. Users may have different amount of Ether requirements; some small amounts and some large amounts during different times. As a result, rather than allowing the user to get a fixed small amount of Ether, a more general distribution mechanism that allows a user to demand and claim arbitrary amounts of Ether, while satisfying fairness among users, is needed. For this end, Max-min Fairness based schemes have been used in centralized settings. Our work contributes a Max-min Fairness based algorithm and its Solidity smart contract implementation that requires low transaction costs independent of the number of users. This is important on the Ethereum blockchain, since a smart contract execution with transaction costs depending on the number of users would mean block gas limit exhaustion problem will eventually be met, making the smart contract ineffective. We report tests which confirm that the low transaction cost aims have been achieved by our algorithm.